2019
Том 71
№ 8

All Issues

Kholyavka O. T.

Articles: 1
Article (Ukrainian)

Hyperbolic Variational Inequality of the Third Order with Variable Exponent of Nonlinearity

Kholyavka O. T.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2014. - 66, № 4. - pp. 518–530

In Sobolev spaces with variable exponent, we consider the problem for a semilinear hyperbolic variational inequality of the third order. We establish conditions for the existence of a solution u of this problem such that u ∈ L ((0, T); V 1,0(Ω)), u t  ∈ L ((0, T); V 1,0(Ω)) ∩ L p(x)(Q T ), and u tt  ∈ L ((0, T); L 2(Ω)), where V 1,0(Ω) ⊂ H 1(Ω).